Approximate Integration

import math
from sympy.parsing.sympy_parser import (parse_expr)


def is_even(x):
  return x % 2 == 0


def left_riemann_sum(a, b, f, n):
  delta_x = (b - a) / n
  sum = 0

  for i in range(n):
    x_i = a + i * delta_x
    sum += delta_x * f(x_i)

  return sum


def right_riemann_sum(a, b, f, n):
  delta_x = (b - a) / n
  sum = 0

  for i in range(1, n + 1):
    x_i = a + i * delta_x
    sum += delta_x * f(x_i)

  return sum


def midpoint_rule(a, b, f, n):
  delta_x = (b - a) / n
  sum = 0

  for i in range(0, n):
    x_i = a + i * delta_x + delta_x / 2
    sum += delta_x * f(x_i)

  return sum


def trapezoidal_approximate_integral(a, b, f, n):
  delta_x = (b - a) / n

  sum = f(a)

  for i in range(1, n):
    x_i = a + i * delta_x
    sum += 2 * f(x_i)

  sum += f(b)

  approx_area = sum * (delta_x / 2)

  return approx_area


def simpsons_rule_approximate_integral(a, b, f, n):
  delta_x = (b - a) / n

  sum = f(a)

  for i in range(1, n):
    x_i = a + i * delta_x
    coefficient = 2 if is_even(i) else 4
    sum += coefficient * f(x_i)

  sum += f(b)

  approx_area = sum * (delta_x / 3)

  return approx_area


def string_to_function(expression):

  def function(x):
    return eval(expression)

  return function


while True:
  print("\nCompute Approximate integral:")
  a = float(eval(input("Area from (a): ")))
  b = float(eval(input("To (b): ")))
  f = string_to_function(input("Of Function: "))
  n = int(input("# of Subintervals (n): "))

  print(f"\nLeft Riemann Sum: {left_riemann_sum(a, b, f, n)}")
  print(f"Right Riemann Sum: {right_riemann_sum(a, b, f, n)}")
  print(f"Midpoint Rule: {midpoint_rule(a, b, f, n)}")
  print(f"\nTrapezoidal: {trapezoidal_approximate_integral(a, b, f, n)}")
  print(f"Simpson's Rule: {simpsons_rule_approximate_integral(a, b, f, n)}")